I have the same problem as everybody else here after I was forced to upgrade Outlook for Mac. Drag&drop between various IMAP-Mailboxes and "On my Computer" (offline) folders worked just fine before the upgrade.
I've played around a bit and found that it's not just the offline folders that are not allowed as a drag&drop destination anymore but also other mail accounts. Moving mails seems to work fine as long as you stay within the account or within the offline folders, but it does no longer work across them.
Not beging able to move mails between different accounts can somehow be seen as "not a bug but a feature". However "On my Computer" is *not* a mail account but a generic offline folder where this limitation makes no sense. Drag&drop should be possible here!
@Microsoft Support:
It would be nice to provide some feedback here. At least acknowledge the issue and let us know if it's been worked on.